Bastia loan Ba from Sunderland
The midfielder joined the Premier League club from Le Havre last July, but failed to establish himself in the first team in his maiden season.
Ba scored on his debut in a 3-1 FA Cup win over Carlisle United in January, but made only two more appearances in the 2013-14 campaign.
First-team opportunities were likely to be limited for the 21-year-old Frenchman in the coming season following the addition of Jack Rodwell.
Ba will instead hope to prove himself with Bastia as they look to build on last season's 10th-place finish under new coach Claude Makelele.
Bastia face Marseille in their Ligue 1 opener on Saturday at the Stade Armand Cesari, where Ba could make his debut for the Corsican club.